Choose your percentage formula
Enter 15 for 15% in these written formulas. Divide by 100 once to turn the rate into a decimal. In Excel, a cell containing 15% already holds 0.15.
| Question | Formula | Example | Check before using |
|---|---|---|---|
| Percentage of a number | rate ÷ 100 × number | 15 ÷ 100 × 200 = 30 | The answer is an amount. |
| Part as a percentage | part ÷ total × 100 | 30 ÷ 200 × 100 = 15% | The total cannot be zero. |
| Find the whole | part ÷ (rate ÷ 100) | 30 ÷ 0.15 = 200 | The percentage cannot be zero. |
| Percentage increase or decrease | (new − original) ÷ original × 100 | (100 − 80) ÷ 80 × 100 = 25% | Use a positive starting value. |
| Percentage difference | absolute gap ÷ average × 100 | 20 ÷ 90 × 100 ≈ 22.22% | Compare non-negative values equally. |
| Percentage points | new percentage − old percentage | 25% − 20% = 5 percentage points | This is a gap between rates. |
| Final price after a discount | original × (1 − rate ÷ 100) | 200 × 0.85 = 170 | A 15% saving is 30, not 170. |
| Final amount after an increase | original × (1 + rate ÷ 100) | 200 × 1.15 = 230 | Add the increase to the original. |
| Original before a discount | final ÷ (1 − rate ÷ 100) | 800 ÷ 0.8 = 1,000 | The discount must be below 100%. |
| Original before an increase | final ÷ (1 + rate ÷ 100) | 1,200 ÷ 1.2 = 1,000 | A 20% rise means a factor of 1.2. |
The ≈ sign marks rounding. For percentage difference, average = (first + second) ÷ 2. If both values are zero, that formula has a zero denominator; our calculator explicitly reports 0% by convention.
Start with the baseline, not the percent sign
80 becomes 100
25% increase
The gain is 20. Divide by the original 80: 20 ÷ 80 × 100.
100 becomes 80
20% decrease
The loss is 20. Divide by the original 100: 20 ÷ 100 × 100.
Compare 80 and 100 equally
≈ 22.22% difference
The gap is 20 and the average is 90. Neither number is chosen as the original.
Mental shortcuts for common percentages
- 10%: divide the number by 10.
- 5%: find 10%, then halve it.
- 1%: divide by 100.
- 15%: add 10% and 5%.
- 25%: divide by four.
- 12.5%: divide by eight.
For 15% of 240, ten percent is 24 and five percent is 12. Add them to get 36. A 15% discount therefore leaves 204.
Three mistakes that change the answer
- Adding a discount back to a sale price. If 800 remains after 20% off, divide by 0.8 to get 1,000. Adding 20% to 800 gives 960 and uses the wrong baseline.
- Adding successive discount rates. A 20% discount followed by 10% off the reduced price leaves 0.8 × 0.9 = 0.72 of the original: a 28% total discount.
- Calling percentage points a relative increase. A rate rising from 20% to 25% gains five percentage points. Relative to 20%, it rises by 25%.
Check a formula with your own numbers
Use the percentage calculator for a single question, the change calculator when you know an old and new amount, or the reverse calculator when you need to recover an original.
For a complete example, see 30 is 15% of what number?. For spreadsheet syntax, use the Excel percentage guide.